"If the solar system … were not moving in orbit around the center, we would fall straight in toward it, arriving a hundred million years from now. But because we do move (at about 150 miles per second) along a nearly circular path …."

"Using a radio telescope system that measures celestial distances 500 times more accurately than the Hubble Space Telescope, astronomers plotted the motion of the Milky Way and found that the sun and its family of planets were orbiting the galaxy at about 135 miles per second.""The sun circles the Milky Way at a speed of about 486,000 miles per hour."

217 km/s

The Sun is one of some 300 billion stars that travel around
the Milky Way in a near circular orbit. These stars are closer
to the galactic center than the Sun. The distance from the center
of our Galaxy to the Sun is about 26,000 light years (a light
year is about 6 trillion miles), which is approximately halfway
out on one of the Milky Way's curving arms. The Sun and its planets
take a period of 225 million years to revolve around the galactic
center. The time it takes for each orbit is sometimes referred
to as a cosmic year or a galactic year. The Sun has completed
about 20 orbits since the solar system was formed. For each orbit,
the Sun traveled 150,000 light years of distance.

The orbit of the Sun around the Milky Way is influenced by
the galaxy's matter, which does not solely occupy the galactic
center. Instead, it is distributed all over space. Some of the
galaxy's mass is inside the sun's orbit and some of it is outside.
The Sun's orbital period is determined by the galaxy's mass within
the orbit of the Sun.

Newton's explanation of the speed of stars in the Milky Way
is as follows. He showed that stars closer to the galactic center,
including the Sun, experience a gravitational pull equal to the
pull created by the mass that is equal to that of all the stars
closer to the galactic center. Hence, the mass of the galactic
center is equal to the total mass of all the stars closer to the
center.

He also showed that stars farther from the center have a combined
gravitational force of zero. Those stars pull in all different
and opposite directions, canceling out one another. Therefore,
the stars closer to the center experience a gravitational pull
towards the center and they move at greater speeds, since there
is more force acting upon them. Conversely, more distant stars
have less force acting upon them and in turn, they travel at lower
speeds. In addition, stars beyond this distance have speeds that
stop decreasing and eventually remain constant.